A341314 Array read by antidiagonals: T(n,k) = (n+k)/gcd(n,k), n>=0, k>=0.

0, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 2, 4, 1, 1, 5, 5, 5, 5, 1, 1, 6, 3, 2, 3, 6, 1, 1, 7, 7, 7, 7, 7, 7, 1, 1, 8, 4, 8, 2, 8, 4, 8, 1, 1, 9, 9, 3, 9, 9, 3, 9, 9, 1, 1, 10, 5, 10, 5, 2, 5, 10, 5, 10, 1, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1, 1, 12, 6, 4, 3, 12, 2, 12, 3, 4, 6, 12, 1

Offset: 0

Author

N. J. A. Sloane, Feb 17 2021

Keywords

• nonn
• tabl

Comments

We define gcd(0,0) = 0.

This sequence arose when studying Reed Kelly's A214551.

Examples

			The array begins:
  0,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ...
  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, ...
  1,  3,  2,  5,  3,  7,  4,  9,  5, 11,  6, 13,  7, ...
  1,  4,  5,  2,  7,  8,  3, 10, 11,  4, 13, 14,  5, ...
  1,  5,  3,  7,  2,  9,  5, 11,  3, 13,  7, 15,  4, ...
  1,  6,  7,  8,  9,  2, 11, 12, 13, 14,  3, 16, 17, ...
  1,  7,  4,  3,  5, 11,  2, 13,  7,  5,  8, 17,  3, ...
  1,  8,  9, 10, 11, 12, 13,  2, 15, 16, 17, 18, 19, ...
  1,  9,  5, 11,  3, 13,  7, 15,  2, 17,  9, 19,  5, ...
  1, 10, 11,  4, 13, 14,  5, 16, 17,  2, 19, 20,  7, ...
  1, 11,  6, 13,  7,  3,  8, 17,  9, 19,  2, 21, 11, ...
  1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,  2, 23, ...
  1, 13,  7,  5,  4, 17,  3, 19,  5,  7, 11, 23,  2, ...
...
The first few antidiagonals are:
  [0]
  [1, 1]
  [1, 2, 1]
  [1, 3, 3, 1]
  [1, 4, 2, 4, 1]
  [1, 5, 5, 5, 5, 1]
  [1, 6, 3, 2, 3, 6, 1]
  [1, 7, 7, 7, 7, 7, 7, 1]
  [1, 8, 4, 8, 2, 8, 4, 8, 1]
  ...
		

Crossrefs

A054531 is a similar sequence. See also A341315, A341316.

Cf. A214551.

Programs

Maple

fa:= (m,n) -> if m=0 and n=0 then 0 else (m+n)/igcd(m,n); fi;
for m from 0 to 12 do lprint([seq(fa(m-n,n),n=0..m)]); od:
for m from 0 to 12 do lprint([seq(fa(m,n),n=0..12)]); od: